Module constructions for certain subgroups of the largest Mathieu group

2019/12/09 by Lea Beneish, Beneish, Lea
Arts and Humanities · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1912.04373

openalex publication_date 2019/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For certain subgroups of M₂₄, we give vertex operator algebraic module constructions whose associated trace functions are meromorphic Jacobi forms. These meromorphic Jacobi forms are canonically associated to the mock modular forms of Mathieu moonshine. The construction is related to the Conway moonshine module and employs a technique introduced by Anagiannis--Cheng--Harrison. With this construction we are able to give concrete vertex algebraic realizations of certain cuspidal Hecke eigenforms of weight two. In particular, we give explicit realizations of trace functions whose integralities are equivalent to divisibility conditions on the number of \mathbbF_p points on the Jacobians of modular curves.

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